WE PROPOSE TO WRITE CODES FOR A FAST EVALUATION OF STEADY, COMPRESSIBLE, TWO-DIMENSIONAL, INVISCID FLOWS, EITHER SUBSONIC OR TRANSONIC, WITH OR WITHOUT BOW SHOCKS AND IMBEDDED SHOCKS. THE COMPUTATIONAL SPEED WILL BE PROVIDED BY A NOVEL SWEEPING TECHNIQUE, BASED ON THE "LAMBDA" INTEGRATION SCHEME. THE CONCEPT HAS ALREADY BEEN SUCCESSFULLY APPLIED TO ONE-DIMENSIONAL PROBLEMS. APPLICATIONS WILL BE MADE TO FLOWS IN DUCTS, AIRFOILS AND BLUNT BODIES IN SUPERSONIC FLIGHT.